A new Method for computing Interest, 53 



The usual formula for compound interest is 



a=P(l4-r)^ (5), 



where r=rate per cent, per annum. 



If we equate the right-hand members of (4) and (5), we have 



Pe'-'«=P(l+r)« (6). 



This is readily reduced to 



e^'=l+r (7). 



Taking the logarithm of both members of (7), we have by a 

 log.(l+r) 

 slight reduction ^'=0-4342944819, &c. (^> 



Equation (8) gives the rate per cent, per annum r', so that the 

 interest being compounded at every instant shall be the same as 

 yearly compound interest at r per cent, per annum. 



By giving to r successively the values 003; 0-03J; 0-04; 

 0-04J; 005; 0-05^; 0-06; 0-06J; 0-07; we find the following 

 values for r' : 



When r=003 we have r'=00295587 



Substituting 0-0676587 for r', and using the well known value 

 of e, equation (11) becomes 



log.a=0-00008050353x<i (12), 

 where d expresses the time in days. 



